In this example we are going to use the Law of Sines
to solve the triangle that we have here
and we will use the Law of Sines
to find the side lengths
little 'b' and little 'c'
we can find the angle Beta
just by doing a bit of arithmetic
so we know that if
we add up all the angles inside of a triangle
they have to equal 180
well if we take 125 degrees
plus 41 degrees
that's going to give us 166 degrees
And if we take 180 degrees
and subtract away 166 degrees
that's going to leave us with 14 degrees
we know that our angle 'Beta'
will equal 14 degrees
so now we can use Law of Sines
to find the side length little 'b' and
little 'c'
we know that
little 'b' over
Sine of Beta
and now we can set up a ratio
err .. another ratio.
we can use another side length
well, we know the side length of 9.72
and then we'll take Sine of
the angle opposite that side
so the angle opposite the side
that has length 9.72
that angle has 125 degrees
we now know Beta
so let's substitute that in
so we have little 'b'
over Sine of Beta
and again we said Beta was 14 degrees
that equals 9.72
divided by Sine of
125 degrees
and to solve for little 'b'
we can multiply both sides by
Sine of 14 degrees
so we'll have that little 'b' equals
9.72
divided by
Sine of
Sine of 125 degrees
multiplied by
Sine of
Sine of 14 degrees
now I'm just going to use my
good-old calculator and
get some values here
I'm going to use as many decimal places
as my calculator has
so 14 ...
erm .. I need to make sure that my
calculator is in degree mode .. OK
so I enter the degree first
Sine of 14 degrees
I'm getting 0.241921896
on my calculator
Sine of 125 degrees
I'm getting 0.819152044
OK so let's just do the multiplication
9.72 x 0.241921896
divided by 0.819152044
I'm getting that to be
2.87
2.87 ... roughly
after rounding to the nearest hundredth
and we can also find
the other side
doing the exact same thing
so we know little 'b' here
that was 2.87
so we've got side little 'c'
over sin of ...
well the angle opposite
well the angle opposite little 'c'
would be Sine of 41 degrees
and again it doesn't matter
which of the other side and ..,
I mean you have to use
a side and its corresponding
opposite angle
I'll just use the same one as before
so we've got 9.72
over Sine of
over Sine of 125 degrees
and we'll do the exact same thing
multiply both sides by
Sine of 41 degrees
so I have Sine of
41 degrees
divided by
Sine of 125 degrees
again being multiplied by
the 9.72
so let's see ...
we said Sine of 125 degrees
that was 0.819152044
we've got 9.72
and let's see ...
Sine of
Sine of 41 degrees here
so there's 41
Sine of that
I'm getting 0.656059029
multiply that
by 9.72
and then divide all of that by
0.819152044
and I'm getting 'c'
to be roughly equal to
to be roughly equal to 7.78
so now we have
all of the side lengths
we also have
all of the angles
so ...
so ... we've now
solved the Triangle.